RESUMO

Many years ago, the gas-phase infrared fundamental intensities of Cl2CS were determined within experimental error from the experimental intensities and frequencies of F2CO, Cl2CO, and F2CS. An additive characteristic substituent shift relationship between atomic polar tensors of these molecules formed the basis for these calculations. Here, QCISD/cc-pVTZ-level Quantum Theory of Atoms In Molecules (QTAIM) individual charge, charge transfer, and polarization contributions to these atomic polar tensor elements are shown to obey the same basic relationship for the extended X2CY (Y = O, S; X = H, F, Cl, Br) family of molecules. QTAIM charge and polarization contributions, as well as the total equilibrium dipole moments of the X2CY molecules, also follow this characteristic substituent shift model. The root-mean-sqaure error for the 231 estimates of these parameters is 0.14 e or only about 1% of the total 10 e range of the Atomic Polar Tensor (APT) contributions determined from the wave functions. The substituent effect APT contribution estimates were used to calculate the infrared intensities of the X2CY molecules. Although one serious discrepancy was observed for one of the CH stretching vibrations of H2CS, accurate values were within 45 km·mol-1 or about 7% of the 656 km·mol-1 intensity range predicted by the QCISD/cc-pVTZ wave functions. Hirshfeld charge, charge transfer, and polarization contributions are also found to follow this model, although their charge parameters do not follow electronegativity expectations.

RESUMO

The Interacting Quantum Atoms (IQA) energy decomposition scheme divides the total energy of a molecule into intra- and interatomic contributions. While the former relates to the kinetic and potential energies of electrons inside a unique individual atomic basin, the latter contains the Coulomb and exchange-correlation potentials between electrons from two atomic basins. Considering that the molecular energy is a sum of IQA contributions, the Hessian matrix can also be written as a sum of "IQA Hessian" matrices, whose elements are second derivatives of IQA terms. Herein, we present a mathematical formalism for the IQA decomposition of force constants revealing their energetic origins. The method consists of adding a new dimension to the Hessian matrix, which becomes 3N × 3N × N2, with N being the number of atoms in the molecule and N2 the number of IQA terms. Since there is no analytical method that produces the IQA second derivatives, the three-dimensional IQA Hessian is numerically calculated. When studying molecular vibrations, force constants, providing information about the nature of chemical bond and related to infrared frequencies, can be obtained by Wilson's FG method, which involves detailed manipulations of the Hessian matrix. In this paper, the methodology is reported and validated for a set of 30 molecules and more than 200 force constants and their interactions. Energetic origins of force constants are presented for diatomics and small molecules containing carbon-carbon, oxygen-oxygen, and carbon-oxygen bonds with different bond orders. It is found that bond stability and stiffness can have strikingly different energetic origins.

RESUMO

Absolute infrared intensities of [Formula: see text] were evaluated with a great variety of DFT and ab initio methods and basis sets. It is shown that the intensities calculated by different levels of theory may not agree with each other even in the qualitative (weak/strong) sense. Geometrical parameters, as well as net atomic charges evaluated from multiple partition schemes, did not vary as much as the intensities and thus cannot explain the tremendous differences found for the latter. As there are no experimental estimates for the intensities to guide the theoretical evaluation, deciding on the best level of theory is reduced to comparisons between the different DFT methods and QCISD or CCSD, believed to be the best theoretical estimates in the set. The differences found among the various DFT methods suggest the development of new methods, instead of converging to a focal point, is rather diverging.

RESUMO

Understanding and controlling polymorphism in molecular solids is a major unsolved problem in crystal engineering. While the ability to calculate accurate lattice energies with atomistic modelling provides valuable insight into the associated energy scales, existing methods cannot connect energy differences to the delicate balances of intra- and intermolecular forces that ultimately determine polymorph stability ordering. We report herein a protocol for applying Quantum Chemical Topology (QCT) to study the key intra- and intermolecular interactions in molecular solids, which we use to compare the three known polymorphs of succinic acid including the recently-discovered γ form. QCT provides a rigorous partitioning of the total energy into contributions associated with topological atoms, and a quantitative and chemically intuitive description of the intra- and intermolecular interactions. The newly-proposed Relative Energy Gradient (REG) method ranks atomistic energy terms (steric, electrostatic and exchange) by their importance in constructing the total energy profile for a chemical process. We find that the conformation of the succinic acid molecule is governed by a balance of large and opposing electrostatic interactions, while the H-bond dimerisation is governed by a combination of electrostatics and sterics. In the solids, an atomistic energy balance emerges that governs the contraction, towards the equilibrium geometry, of a molecular cluster representing the bulk crystal. The protocol we put forward is as general as the capabilities of the underlying quantum-mechanical model and it can provide novel perspectives on polymorphism in a wide range of chemical systems.

RESUMO

A novel IRC-TS-CCTDP method to investigate transition states (TS) is proposed in which changes in the molecular geometry follow atomic displacements corresponding to the imaginary frequency normal coordinate. Electronic charge structure changes can be analyzed using the charge-charge-transfer-dipolar polarization (CCTDP) model. An application is presented for the gas-phase SN2 reaction transition state structures for nine NuCX3LG- systems, with Nu and LG = H, F, Cl and X = H, F. Using quantum theory of atoms in molecules (QTAIM) at the QCISD/aug-cc-pVTZ level, atomic charges and atomic dipoles were obtained and applied to calculate the CCTDP contributions to their imaginary normal mode intensities. The results show that the imaginary bands are exceptionally strong, ranging from 1217 to 16 086 km·mol-1, much higher than the stretching intensities found in the methyl halides (that are all less than 100 km·mol-1). For all systems, the CT contributions are responsible for 63% of the total dipole moment derivatives. The charge contributions are slightly higher for transition states where X = F. Dipolar polarization contributions are always small and only reflect the molecular orientation change when the nucleophile displaces the leaving group and, therefore, can be neglected. The same occurs for contributions from the X atoms. Only atoms aligned with the reaction axis Nu--C-LG contribute to the total intensity. Almost all of the infrared intensities are determined by electron transfers from the nucleophile to carbon and subsequently from carbon to the leaving group. The mechanism of charge transfer revealed by the CCTDP model is consistent with the well-accepted reaction mechanism. Open-access codes for performing the IRC-TS-CCTDP analysis are described and provided for potential users in the Supporting Information.

RESUMO

The reaction path for the formation of BX3-NH3 (X = H, F, Cl, Br) complexes was divided into two processes: (i) rehybridization of the acid while adopting a pyramidal geometry, and (ii) the complex formation from the pyramidal geometries of the acid and base. The interacting quantum atom (IQA) method was used to investigate the Lewis acidity trend of these compounds. This topological analysis suggests that the boron-halogen bond exhibits a considerable degree of ionicity. A relative energy gradient (REG) analysis on IQA energies indicates that the acid-base complex formation is highly dependent on electrostatic energy. With increasing halogen electronegativity, a higher degree of ionicity of the B-X is observed, causing an increase in the absolute value of X and B charges. This increases not only the attractive electrostatic energy between the acid and base but also enhances the repulsive energy. The latter is the main factor behind the acidity trend exhibited by trihalides. Changes in geometry are relevant only for complexes where BH3 acts as an acid, where lower steric hindrance facilitates the adoption of the pyramidal geometry observed in the complex. The CCTDP analysis shows that infrared intensities of BX3-NH3 are determined mostly by the atomic charges and not by the charge transfer or polarization. The opposite is observed in covalent analogues.

RESUMO

Generalized atomic polar tensor (GAPT) has turned into a very popular charge model since it was proposed three decades ago. During this period, several works aiming to compare different partition schemes have included it among their tested models. Nonetheless, GAPT exhibits a set of unique features that prevent it from being directly comparable to "standard" partition schemes. We take this opportunity to explore some of these features, mainly related to the need of evaluating multiple geometries and the dynamic character of GAPT, and show how to obtain the static and dynamic parts of GAPT from any static charge model in the literature. We also present a conceptual evaluation of charge models that aims to explain, at least partially, why GAPT and quantum theory of atoms in molecules (QTAIM) charges are strongly correlated with one another, even though they seem to be constructed under very different frameworks. Similar to GAPT, infrared charges (also derived from atomic polar tensors of planar molecules) are also shown to provide an improved interpretation if they are described as a combination of static charges and changing atomic dipoles rather than just experimental static atomic charges.

Assuntos

RESUMO

We present a complete theoretical protocol to partition infrared intensities into terms owing to individual atoms by two different but related approaches: the atomic contributions (ACs) show how the entire molecular vibrational motion affects the electronic structure of a single atom and the total infrared intensity. On the other hand, the dynamic contributions (DCs) show how the displacement of a single atom alters the electronic structure of the entire molecule and the total intensity. The two analyses are complementary ways of partitioning the same total intensity and conserve most of the features of the total intensity itself. Combined, they are called the AC/DC analysis. These can be further partitioned following the CCTDP (or CCT) models according to the population analysis chosen by the researcher. The main conceptual features of the equations are highlighted, and representative numerical results are shown to support the interpretation of the equations. The results are invariant to rotation and translation and can readily be extended to molecules of any size, shape, or symmetry. Although the AC/DC analysis requires the choice of a charge model, all charge models that correctly reproduce the total molecular dipole moment can be used. A fully automated protocol managed by the Placzek program is made available, free of charge and with input examples.

RESUMO

Out-of-plane CH group bending vibrational bands have long been known to be more intense than those for CF groups in similar molecular environments. This contrasts with expectations derived from charge models for which equilibrium atomic charge displacements are considered dominant contributions to dipole moment change on vibration. For this reason, the Charge, Charge Transfer, Dipolar Polarization (CCTDP) model based on the Quantum Theory for Atoms in Molecules (QTAIM) has been applied to the ethylene, tetrafluoroethylene and difluoro- and dichloroethylene molecules. Atomic charges and atomic dipoles from QTAIM and infrared intensities were calculated at the M06-2X/aug-cc-pVTZ level. The CH out-of-plane bending vibrations with relatively high intensities between 48.0 and 82.1 km/mol are characterized by small atomic charge and large polarization contributions having the same sign resulting in large net dipole moment contributions. Large charge and polarization dipole moment derivative contributions with opposite signs cancel each other producing very small intensities between 0.3 and 12.7 km/mol for the CF bends. Intensity variations can be successfully modeled by only their carbon atomic contributions with smaller contributions from the terminal atoms. Both CH and CF bending vibrations have large polarization contributions. Their charge contributions are usually small except for carbon atoms bonded to two fluorine atoms. The terminal atoms as well as the carbons have charge and polarization contributions of opposite sign. Comparison to benzene and hexafluorobenzene reveals that changes in these molecules' electronic densities caused by the out-of-plane atomic displacements are characteristic for each bond. In conclusion, successful modeling of the ethylene intensities must include atomic dipole parameters.Models based only on charges are doomed to failure.

RESUMO

Atomic charges are invariant for out-of-plane distortions, making their molecular vibrations enticing for electronic structure studies. Of planar molecules, the boron trihalides contain some of the most polar bonds known to chemistry, although their out-of-plane bending intensities are very small contrary to expectations from atomic charge models. Here, the out-of-plane infrared intensities of the BX(2)X(3)X(4) (X(2), X(3), X(4) = H, F, Cl, Br) molecules are investigated using quantum theory of atoms in molecules atomic charges and atomic dipoles within the formulism of the charge, charge transfer, dipolar polarization model at the QCISD/aug-cc-pVTZ quantum level. Dipole moments induced by equilibrium charge displacement of atoms perpendicular to the molecular plane are almost completely cancelled by their electronic density polarizations. The calculated boron trihalide intensities are small for molecules with such polar bonds ranging from 0.6 to 106.1 km mol-1. Even though the Cl atomic charge of -0.72 e in BCl3 is more negative than the hydrogen values of -0.67 e in BH3, the hydride out-of-plane intensity of 82.0 km mol-1 is an order of magnitude larger than that of the trichloride, 6.3 km mol-1. Owing to their diverse electronic structures, transference of atomic charges and dipole parameters among the boron trihalides is extremely challenging and does not result in accurate intensity values. For this reason, a machine-learning decision-tree algorithm was used to perform the transference procedure. Decision trees were optimized using quantum-level intensity values. Atomic charge and dipole parameters were estimated for a set of 12 test set molecules. These parameters provided intensity estimates with a root-mean-square error of 2.1 km mol-1 compared with QCISD/aug-cc-pVTZ reference values.

RESUMO

The largest source of experimental error in determining gas phase fundamental infrared intensities arises from the separation of overlapped bands. Quantum chemical calculations at the QCISD/cc-pVTZ and QCISD/aug-cc-pVTZ levels were carried out on four simple hydrocarbons and the fluoro- and chloromethanes with the aim of accurate overlapped band separation. Fundamental vibrational intensity results were compared with individual empirical intensity estimates reported for overlapped band systems. Root mean square differences of 3.7 km mol-1 are found between the experimental and QCISD/cc-pVTZ values for nine overlapped bands of the hydrocarbons and 11.8 km mol-1 for the QCISD/aug-cc-pVTZ values for 12 overlapped bands of the fluoro- and chloromethanes. These values correspond to 14% and 18% of the average hydrocarbon and halomethane intensity values. Previous experimental separation errors were estimated to be quite larger, between 20% and 50%. As quantum calculations are continuously being refined one can expect more accurate band separation results in the future.

RESUMO

Infrared band intensification of the A-H bond stretching mode of A-H···B acid-base systems has long been known to be the most spectacular spectral change occurring on hydrogen bonding. A QTAIM/CCTDP model is reported here to quantitatively explain the electronic structure origins of intensification and investigate the correlation between experimental enthalpies of formation and infrared hydrogen bond stretching intensifications amply reported in the literature. Augmented correlation-consistent polarized triple-zeta quantum calculations at the MP2 level were performed on complexes with HF and HCl electron acceptors and HF, HCl, NH3, H2O, HCN, acetonitrile, formic acid, acetaldehyde, and formaldehyde electron donor molecules. The A-H stretching band intensities are calculated to be 3 to 40 times larger than their monomer values. Although the acidic hydrogen atomic charge is important for determining the intensities of HF complexes relative to HCl complexes with the same electron donor, they are not important for infrared intensifications occurring on hydrogen bond formation for a series of bases with a common acid. Charge transfers are found to be the most important factor resulting in the intensifications, but dipolar polarization effects are also significant for each series of complexes. A mechanism involving intra-acid and intermolecular electron transfers as well as atomic polarizations is proposed for understanding the intensifications. The calculated sums of the intermolecular electron transfer and acid dipolar polarization contributions to the dipole moment derivatives for each series of complexes are highly correlated with their enthalpies of formation and H-bond intensifications. This could be related to increasing electron transfer from base to acid that correlates with the calculated hydrogen bonding energies and may be a consequence of the A-H bond elongation on complex formation having amplitudes similar to those expected for the A-H vibration.

RESUMO

New experimental intensity results obtained by band integration from the PNNL (Pacific Northwest National Laboratory) spectral library are reported for 26 CH vibrations of methane, acetylene, ethylene, ethane, allene, propyne and cyclopropane. The PNNL intensity values range from 3.1 to 185.4 km mol-1 and are in excellent agreement, rms difference of 3.1 km mol-1, with earlier low resolution intensity results. QCISD/6-311++G(3d,3p) and QCISD/cc-pVTZ theoretical results are in good agreement with the PNNL intensity values with rms differences of 4.4 and 4.9 km mol-1, respectively. Charge-charge transfer-dipolar polarization model parameters at both quantum levels indicate that the charge transfer-dipolar polarization contributions to the intensities are much larger than those owing to the movements of static equilibrium charges on hydrogen for these vibrations except for the CH vibrations of acetylene that is known to contain very acidic hydrogen atoms. The main effect of the static charge movement comes from its interaction with charge transfer-dipolar polarization owing to the relatively large parameter values of this dynamic electronic contribution. The sum of the charge transfer-dipolar polarization parameters with their interaction with the charge accurately describes the variations in the intensity values of these hydrocarbon vibrations.

RESUMO

New experimental values of the fundamental infrared gas phase intensities of the fluorochloromethanes have been determined by integrating the areas of vibrational bands contained in the PNNL spectral library using homemade software. The root mean square differences of these values and averages of experimental values determined at lower resolution during the latter part of the 20th century is 26.6 km mol-1. All but one of the low resolution intensities are smaller than the PNNL values. The exception is the ν1,ν4 overlapped band intensity of CF3Cl that has a standard deviation of the low resolution values of ±112.5 km mol-1, larger than the observed difference of 102.5 km mol-1. The use of an augmented triple zeta basis set at the QCISD level results in an rms difference of only 8.4 km mol-1 for the fluoro- and chloromethane PNNL intensities, whereas a comparison of these with results at the QCISD/cc-pVTZ level produces an error twice as large, 16.2 km mol-1. As such these results suggest that future comparisons of theoretical intensities with experimental values should take into account integrated intensities that can be obtained from hundreds of spectra in the PNNL library. Furthermore, the intensity values obtained from the PNNL spectra confirm electronegativity model results previously reported based on the low resolution intensities.

RESUMO

The robustness of the QTAIM charge-charge transfer-dipolar polarization parameters for the CH, CF, and CCl stretching and bending distortions of the fluoro- and chloromethanes was determined comparing results calculated at three quantum levels, MP2/6-311G++(3d,3p), QCISD/cc-pVTZ, and QCISD/aug-cc-pVTZ. The correlation coefficients between the MP2/6-311G++G(d,p) and QCISD/cc-pVTZ results with those of QCISD/aug-cc-pVTZ intensities are excellent, 0.934 and 0.988, respectively, showing that the parameters converge with increasing quality of the quantum levels. In spite of numerical differences, the interpretation of the electronic structure changes occurring for these vibrations is the same for all three quantum levels. Accurate determination of charge transfer-counterpolarization effects is important for properly describing electron density changes for small molecular distortions.

RESUMO

Fundamental infrared vibrational transition intensities of gas-phase molecules are sensitive probes of changes in electronic structure accompanying small molecular distortions. Models containing charge, charge transfer, and dipolar polarization effects are necessary for a successful classification of the C-H, C-F, and C-Cl stretching and bending intensities. C-H stretching and in-plane bending vibrations involving sp3 carbon atoms have small equilibrium charge contributions and are accurately modeled by the charge transfer-counterpolarization contribution and its interaction with equilibrium charge movement. Large C-F and C═O stretching intensities have dominant equilibrium charge movement contributions compared to their charge transfer-dipolar polarization ones and are accurately estimated by equilibrium charge and the interaction contribution. The C-F and C-Cl bending modes have charge and charge transfer-dipolar polarization contribution sums that are of similar size but opposite sign to their interaction values resulting in small intensities. Experimental in-plane C-H bends have small average intensities of 12.6 ± 10.4 km mol-1 owing to negligible charge contributions and charge transfer-counterpolarization cancellations, whereas their average out-of-plane experimental intensities are much larger, 65.7 ± 20.0 km mol-1, as charge transfer is zero and only dipolar polarization takes place. The C-F bending intensities have large charge contributions but very small intensities. Their average experimental out-of-plane intensity of 9.9 ± 12.6 km mol-1 arises from the cancellation of large charge contributions by dipolar polarization contributions. The experimental average in-plane C-F bending intensity, 5.8 ± 7.3 km mol-1, is also small owing to charge and charge transfer-counterpolarization sums being canceled by their interaction contributions. Models containing only atomic charges and their fluxes are incapable of describing electronic structure changes for simple molecular distortions that are of interest in classifying infrared intensities. One can expect dipolar polarization effects to also be important for larger distortions of chemical interest.

RESUMO

Dynamic atomic contributions (DACs) to the infrared intensities of 14 amino acids have been transferred to three peptide molecules, glycylglycine, trialanine, and the melanocyte-inhibiting factor MIF-1, to estimate the infrared intensities of the most strategic peptide bands. The DACs of the amino acids and infrared intensities of the peptides were determined at the DFT B3LYP/6-311+(d,p) level. The Quantum Theory of Atoms In Molecules (QTAIM) Charge-Charge Transfer-Dipolar Polarization (CCTDP) model at this Density Functional Theory (DFT) level was used to classify the O-H, NH2, N-H, and C═O stretching as well as the NH2 bending characteristic groups for use in the transference procedure. Contrary to the frequencies, the intensities within these groups can have very diverse values, although their electronic structure changes upon vibration have predictable QTAIM behaviors for each group. Compared to the DFT calculated values, the two transferred O-H stretching intensities of the peptides are estimated with a root-mean-square (rms) error of 19.1 km mol-1. Six NH2 symmetric and antisymmetric stretching intensities were determined with a 9.9 km mol-1 error. The eight estimated C═O stretching bands have a rms error of 78.0 km mol-1 or 23.6% of the average DFT peptide C═O intensity of 328.4 km mol-1. The proposed procedure is applicable to experimental infrared intensities if a calibration set of molecules with known atomic polar tensors and normal coordinate transformations is available.